f(x) = sinx+cosx/sinx-cosx производная

Вопрос школьника по предмету Алгебра

f(x) = sinx+cosx/sinx-cosx производная

Ответ учителя по предмету Алгебра

f′(x)=(sin(x)+cos(x)/sin(x)−cos(x))′=
=(sin(x)+cos(x))′⋅(sin(x)−cos(x))−(sin(x)+cos(x))⋅(sin(x)−cos(x))′/(sin(x)−cos(x))^2=
=((sin(x))′+(cos(x))′)⋅(sin(x)−cos(x))−(sin(x)+cos(x))⋅((sin(x))′−(cos(x))′)/(sin(x)−cos(x))^2=
=(cos(x)+(−sin(x)))⋅(sin(x)−cos(x))−(sin(x)+cos(x))⋅(cos(x)−(−sin(x)))/(sin(x)−cos(x))^2